Question

section 5.2 homework
score: 3/15 answered: 3/15
question 4
find the indicated probability
given
p(a) = 0.3
p(b) = 0.4
p(a or b) = 0.7
find
p(a and b) =
are these events disjoint?
yes
no

Explanation:

Step1: Recall probability formula

Use the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$.

Step2: Rearrange formula to solve for $P(A\ and\ B)$

$P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)$.

Step3: Substitute given values

$P(A\ and\ B)=0.3 + 0.4-0.7$.

Step4: Calculate result

$P(A\ and\ B)=0$.

Step5: Determine if events are disjoint

Disjoint events have $P(A\ and\ B) = 0$. Since $P(A\ and\ B)=0$, the events are disjoint.

Answer:

$P(A\ and\ B)=0$
Yes